Are there any other ways of decomposing 1/11 into sum of two unit fractions? In how many ways can we write 1/60 ass a sum of two unit fractions? More generally, in how many ways can the unit fraction 1/n be written as the sum of two unit fractions? In other word, how many ordered pairs (a, b) of positive integers a, b are there for which                                  1/n = 1/a + 1/b?

Q: (a) Express the following continued fractions as rational numbers in lowest terms. [0; 2, 3, 4, 2] 1…

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Q: Find the first three terms of the expansion (4 – 2x)³.

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Q: If Given X1=12 X2=19 X3=10 X4=7, then the summation of X equals?

A: The given values are X1=12,X2=19,X3=10,X4=7. The summation of X equals, ∑X=X1+X2+X3+X4=12+19+10+7=48

Q: 13/52 as a reduced fraction

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Q: Consider the set of all fractions equal to12. If you take any10 of those fractions, add their…

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Q: n 1. A unit fraction is a fraction of the form where n is a positive integer. Note that the unit…

A: It is given that the unit fraction  can be written as the sum of two unit fractions in the given…

Q: Machine A Can Assemble ce product in 2 hours while machine B Can Assemble the same product in 3…

A: Given that a machine A  can assemble a product in  hours . and machine B can assemble a product in…

Q: 7. Use the properties of the operations of rational number arithmetic to perform these calculations.…

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Q: how do we go from 1/2(1-1/256) divided by 3/2 to 1/3(255/256)

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Q: 4 0 0 0 0 0 2 0 0 0 Evaluate 0 0 4 0 0. 0 0 0 1 0 0 0 0 0 6 4 0 0 0 0 0 2000 0 0 4 0 0 = 0 0 0 1 0 0…

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Q: The following expressions are called continued fractions: 1 + 1 + - 1 + 1 + 1 + - 1 + 1 + 1 1 + 1 +…

A: Given: 1+1x, 1+11+1x, 1+11+11+1x,  1+11+11+11+1x To simplify each expression

Q: Show that if the simple continued fraction expression of the rational number α, α > 1, is [a0;…

A: Remark : In the question, the reciprocal has a missing element. I am providing the solution with…

Q: Let n be a positive integer. Find the continued fraction expansion for √n(n + 1).

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Q: Find the sum of 1/7 + 3/7 + 32/7 + 32 /7 + ⋅⋅⋅ + (3)n-1 / 7

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Q: (1/(3-5)} + {1/(5-7)} + {1/(7 · 9))} +......+ 1/{(2n + 1)(2n + 3)} = (a) n/(2n + 3) (b) n/(2(2n +…

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Q: Use al-Kashi's method to approximate 138 (including the fractional part of the approximation).

A: In the solution part given the complete explanation of the solution by using al-Kashi's method

Q: 3. Obtaining Common Denominators: If each part of the bar is split into 4 equal parts and each part…

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Q: Find S9 for the series 7 + (-21) + 63 + (-189) + ...

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Q: Express 8/9 as a sum of distinct unit fractions and express your answer in Greek notation. This…

A: We have expressed 8/9 it as a sum of distinct unit fractions and also we have to express the answer…

Q: You should have observed that the general pattern using the fractional format is: 2n 8642 I(n) = 2…

A: We have given a series I(n)We have to observe and rewrite in general pattern

Q: +2= %3D

A: We will use the concept of fraction division : ab divided by cd means abmultiply by dc i.e.…

Q: Use the formula for the sum of the first n integers and/or the formula for the sum of a geometric…

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Q: The identity formula we have been using is 1/n= 1/(n+1) + 1/n(n+1).  Here is the problem at hand:…

A: We need to use given identity twice to represent the unit fraction  in three term

Q: if ACB, P(A)=1/4, and P(B)=1/3, find P(A/B) and P(BA)

A: Given A⊂B  P(A)=1/4, P(B)=1/3

Q: Find the total length of the hypocycloid x2/3 + y2/3 = 52/3 (Use symbolic notation and fractions…

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Q: X/n where n ={1,2,3,4,5,6, } find the smallest X so that you will get remainder n-1 ....

A: To find the smallest X which when divided by a set of numbers n will yield a particular remainder,…

Q: Since money and percent are both based on 100, it is easy to think in terms of money and convert to…

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